Question

savanah solved the equation 3+4 multiplied by the absolute value of x/2+3=11 for one solution. her work is shown below. what is the other solution to the given absolute value equation: savanah's solution was x= -2

Answer 1

Answer:

-10

Step-by-step explanation:

Given the equation solved by savanah expressed as $3+4|\frac{x}{2} + 3| = 11$, IF she solved for one of the solution and got x = -2, we are to solve for the other value of x.

Note that the expression in modulus can be expressed as a positive expression and negative expression.

For the positive value of the expression $|\frac{x}{2} + 3|$ i.e $\frac{x}{2} + 3$, the expression becomes;

$3+4(\frac{x}{2} + 3) = 11$

On simplification;

$3+4(\frac{x}{2} + 3) = 11\\\\3 + 4(\frac{x}{2} )+4(3) = 11\\\\3 + \frac{4x}{2}+ 12 = 11\\\\3 + 2x+12 = 11\\\\2x+15 = 11\\\\Subtract \ 15 \ from \ both \ sides\\\\2x+15-15 = 11-15\\\\2x = -4\\\\x = -2$

For the negative value of the expression $|\frac{x}{2} + 3|$ i.e $-(\frac{x}{2} + 3)$, the expression becomes;

$3+4[-(\frac{x}{2} + 3)] = 11$

On simplifying;

$3+4[-(\frac{x}{2} + 3)] = 11\\\\3+4(-\frac{x}{2} - 3)= 11\\\\3-4(\frac{x}{2}) -12 = 11\\\\3 - \frac{4x}{2} - 12 = 11\\\\3 - 2x-12 = 11\\\\-2x-9 = 11\\\\add \ 9 \ to \ both \ sides\\\\-2x-9+9 = 11+9\\-2x = 20\\\\x = -20/2\\\\x = -10$

Hence her other solution of x is -10